The impact of perceived strength in the war of attrition

Abstract

In a war of attrition a player's perceived strength is the distribution describing beliefs about her valuation. Small asymmetries in strength have a large effect: in the unique equilibrium of a game with a deadline the war ends quickly (instantly, as the deadline becomes infinite) with a concession by the (perceived) weaker player. The ranking of strength compares hazard rates in the upper tails of the distributions of beliefs; greater uncertainty about a player tends to give her more strength. The results also hold if techniques other than a deadline are used to obtain a unique equilibrium.